User manual SPSS TRENDS 10.0

[. . . ] SPSS Trends 10. 0 TM For more information about SPSS® software products, please visit our WWW site at http://www. spss. com or contact Marketing Department SPSS Inc. 233 South Wacker Drive, 11th Floor Chicago, IL 60606-6307 Tel: (312) 651-3000 Fax: (312) 651-3668 SPSS is a registered trademark and the other product names are the trademarks of SPSS Inc. No material describing such software may be produced or distributed without the written permission of the owners of the trademark and license rights in the software and the copyrights in the published materials. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subdivision (c)(1)(ii) of The Rights in Technical Data and Computer Software clause at 52. 227-7013. [. . . ] It says that the change in Crest market share at time t--the left side of the equation--equals the disturbance at time t minus some fraction () of the disturbance at time t-1. Creating Intervention Variables Now that you have a linear equation for the market share at any time prior to the ADA endorsement, you must figure out a way to incorporate a term for the endorsement itself--the "intervention, " as it is called. Figure 10. 4 shows values of the market-share series around the time of the endorsement. 138 Chapter 10 Figure 10. 4 Data values for weeks 130 through 140 You would like to pinpoint precisely when the effect of the endorsement showed up in the market shares of both toothpastes. From the listing of the two series you can see that the Crest market share was volatile during this period; it jumped up in week 135 and again in week 136, seemed to settle back, and then resumed its high level. The Colgate share dropped sharply in week 135 and again in week 136, and then basically remained at its new, low level. A simple model would say that the effect showed up over the two weeks 135 and 136, perhaps in two stages. Dummy Variables A variable or series that has only the values 0 or 1 is called a dummy variable. You can easily include a dummy variable in a model--just write it into the equation, with a coefficient of its own. Here we call the coefficient : Market share = rest of model + ( dummy ) You want a dummy variable that reflects the presence or absence of the intervention. Then × dummy equals 0 and the predicted market share is given by the rest of the model. Starting with week 135, dummy should equal 1 and the prediction becomes (rest of the model) + . By using the dummy variable you can thus produce a "step" in the prediction--regardless of what the rest of the model involves. An Effective Decay-Preventive Dentifrice: Intervention Analysis 139 The coefficient must be estimated along with all the rest of the coefficients in the model. When is positive, the step goes up (like Crest market share in week 135); when is negative, the step goes down (like Colgate market share in week 135). To represent the ADA endorsement, whose effect occurred over a two-week period, you need two dummy variables, one for week 135 and one for week 136. Each will have a coefficient that indicates the effect of the endorsement in that week. The equation for the model becomes ( 1 ­ B )crest t = ( 1 ­ B )disturbance t + 1 dummy1 + 2 dummy2 Equation 10. 2 Before you can estimate the coefficients of the dummy variables, you must decide how to build them. In order to work as described above, they must equal 0 when the intervention is not present and 1 when the intervention is present. Steps and Pulses The most common types of dummy variables in time series analysis are step functions and pulse functions. A step function is 0 until some crucial moment comes, when it "steps" immediately to 1. A pulse function similarly jumps to 1 at a crucial moment but then returns immediately to 0 and remains there. When you represent step and pulse functions by the values of a time series, the relationship between the two is clear: · The differences in a step variable form a pulse variable. (All the differences are 0 except when the step occurs, and that difference is 1--so the differences are a pulse variable. ) · The cumulative total of a pulse variable makes a step variable. (The cumulative total starts as 0, becomes 1 at the time of the pulse, and then never changes. ) You can easily create variables representing steps or pulses in SPSS using the Compute Variable dialog box. [. . . ] There have been subsequent corrections to them, however, as published in Farebrother, Econometrica 48(6): 1554 and Econometrica 49(1): 277. The corrections are as follows: Durbin-Watson Significance Tables 283 Table A. 1 Corrections for Table A. 2--Table A. 7 k n Bound Incorrect Correct Table A. 2 6 8 9 10 10 18 10 75 75 75 40 75 80 40 dU dU dU dL dU dU dL 1. 646 1. 716 1. 746 0. 789 1. 785 2. 057 0. 945 1. 649 1. 714 1. 748 0. 749 1. 783 2. 059 0. 952 Table A. 3 k n Bound Incorrect Correct Table A. 4 Table A. 5 0 8 19 8 10 14 1 3 8 7 15 90 70 200 34 39 15 14 0. 389 9. 185 1. 617 2. 089 1. 116 1. 295 2. 645 2. 432 0. 984 0. 398 0. 185 1. 167 2. 098 2. 116 1. 296 2. 615 2. 423 0. 948 Table A. 6 Table A. 7 284 Appendix A Table A. 2 Models with an intercept (from Savin and White) Durbin-Watson Significance Tables 285 Table A. 3 Models with an intercept (from Savin and White) Reprinted, with permission, from Econometrica 45(8): 1992-1995. 286 Appendix A Table A. 4 Models with no intercept (from Farebrother): Positive serial correlation Durbin-Watson Significance Tables 287 Table A. 5 Models with no intercept (from Farebrother): Positive serial correlation Reprinted, with permission, from Econometrica 48(6): 1556-1563. 288 Appendix A Table A. 6 Models with no intercept (from Farebrother): Negative serial correlation Durbin-Watson Significance Tables 289 Table A. 7 Models with no intercept (from Farebrother): Negative serial correlation Appendix B Guide to ACF/PACF Plots The plots shown here are those of pure or theoretical ARIMA processes. Here are some general guidelines for identifying the process: · Nonstationary series have an ACF that remains significant for half a dozen or more lags, rather than quickly declining to zero. You must difference such a series until it is stationary before you can identify the process. [. . . ]